Heart valve insufficiency typically involves regurgitation of blood through a heart valve that is unable to close completely or properly, resulting in impaired cardiovascular function. Valvular insufficiency may affect, for example, the mitral valve, the aortic valve, or the tricuspid valve, and can be associated with calcified or prolapsed leaflets, and/or expansion or deformation of the valve annulus. One method of treating heart valve insufficiency is to employ one or more leaflet clips to improve coaptation of the native valve leaflets. However, conventional leaflet clips can be difficult to implant, can interfere with the function of or damage associated valve structures such as chordae, and are frequently limited to use with a single type of heart valve. Accordingly, improvements to devices and methods of treating heart valve insufficiency are desirable.